No major change. It is artillery and machineguns which do the killing.
Nevertheless it shows how the French were in the forefront of military tech development.
Chapeux bas!
From when I looked up casualty stats it was in 1916 that artillery overtook small arms in terms of casualty infliction. In more mobile fighting it is more mobile weapons that do the majority of killing/wounding. MGs of course are more effective at that, but they were not all that common until 1916 as well and so heavy that they were more defensive weapons than offensive. So having more effective rifles and a 10-15 round internal magazine would be pretty important in 1914 and '15 before fire and movement tactics because standard.
Having a lighter, lower recoiling, more long range cartridge in service before the war would give the French a pretty important advantage as well, much like how the Spanish 7mm Mausers made them much more effective in the Spanish-American war than the US forces. That and all the above making MGs easier to make lighter and more efficient. Can you imagine how much better the Chauchat would have been without rimmed cartridges and the brutal recoil of the 8mm Lebel? Actually come to think of it the Chauchat might have been a pretty darn decent auto-rifle with better ammo.
In 1914 machine guns were crew served and semi-auto pretty much doubles or triples the maximum rate of fire when compared to something manually cycled like a bolt-action rifle.
Indeed and given the tactics of the day the high rate of fire and lower recoil, plus ability to carry more ammo would have been a massive advantage.
Biggest change would be, IMO, the new cartridge. The 8mm Lebel was rather unsuited for automatic fire(rimmed cartridge, bottleneck angles made automated feeding and extraction complicated). A newer cartridge may lead to a better machine gun earlier than the post-war Chatellerault.
Indeed, the Chauchat would be highly interesting with a 7mm Mauser-like cartridge. In fact it might have been available in 1914 without having to design around the 8mm Lebel, since development started in 1903 and took until 1914 to get into first production. Having box magazines, like the .30-06 version, would have fixed a lot of the unreliability issues, as the French claimed 2/3rds of stoppages were caused by the half moon, open magazines and troops greasing the magazines to get the 8mm Lebel cartridges to feed properly.
Rimmed cartridges can be designed around (Bren gun obviously), but they are a nightmare to engineer a design to get to work properly.
So for everyone what about the influence it could/would have on other countries during and after the war? Let's assume the general course of the war and outcome are the same.
IMHO the US would jump on the .276 Pedersen ammo much more quickly once they experienced the 7mm Chauchat, so we could see the Pedersen rifle or .276 Garand considerably sooner than OTL development. The British would follow as they planned on adopting it if the US did so they could maintain commonality of ammo in case of another war so they could ensure supply lines would be more efficient/cheaper.
So we could see a US battle rifle with a box magazine and select fire capabilities before WW2 in .276 Pedersen, which would remove the need for the BAR and could well end up being a viable version of the M14 considering the cartridge was lower powered, so had substantially less recoil and heat build up.
The Germans too might adopt their 7x46mm or 39mm (two different designs) interwar cartridges that they were experimenting with since all the cool kids were doing it. The Soviets being Soviets would likely keep what they had to save money for the 5 year plans. The Italians and Japanese already had their own 6.5mm designs, so no need to change much.
A 7x46mm MG42 sounds quite interesting, especially since it would be made significantly lighter due to the lower powered cartridge. Same with a .276 Bren gun.